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%I #22 Jun 26 2022 23:50:44
%S 31,156,811,1778,15035,31848,174275,903223,56174101,281773728,
%T 1465042741,3211859210,27159916421,57531692052,314818376681,
%U 1631623575457,101475480055015,509009023850532,2646520599307675,5802050222465882,49062922379034731,103927894980535344
%N Numerators of continued fraction convergents to sqrt(973).
%H Vincenzo Librandi, <a href="/A042882/b042882.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 1806446, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: (31 + 156*x + 811*x^2 + 1778*x^3 + 15035*x^4 + 31848*x^5 + 174275*x^6 + 903223*x^7 + 174275*x^8 - 31848*x^9 + 15035*x^10 - 1778*x^11 + 811*x^12 - 156*x^13 + 31*x^14 - x^15)/(1 - 1806446*x^8 + x^16). - _Vincenzo Librandi_, Dec 08 2013
%F a(n) = 1806446*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 08 2013
%t Numerator[Convergents[Sqrt[973], 30]] (* or *) CoefficientList[Series[(31 + 156 x + 811 x^2 + 1778 x^3 + 15035 x^4 + 31848 x^5 + 174275 x^6 + 903223 x^7 + 174275 x^8 - 31848 x^9 + 15035 x^10 - 1778 x^11 + 811 x^12 - 156 x^13 + 31 x^14 - x^15)/(1 - 1806446 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 08 2013 *)
%t LinearRecurrence[{0,0,0,0,0,0,0,1806446,0,0,0,0,0,0,0,-1},{31,156,811,1778,15035,31848,174275,903223,56174101,281773728,1465042741,3211859210,27159916421,57531692052,314818376681,1631623575457},40] (* _Harvey P. Dale_, Jul 04 2017 *)
%o (Magma) I:=[31,156,811,1778,15035,31848,174275,903223,56174101,281773728, 1465042741,3211859210,27159916421,57531692052,314818376681, 1631623575457]; [n le 16 select I[n] else 1806446*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Dec 08 2013
%Y Cf. A042883.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Vincenzo Librandi_, Dec 08 2013
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